## What is Cost of Debt (Kd)?

Cost of debt is the expected rate of return for the debt holder and is usually calculated as the effective interest rate applicable to a firms liability. It is an integral part of the discounted valuation analysisDiscounted Valuation AnalysisDiscounted cash flow analysis is a method of analyzing the present value of a company, investment, or cash flow by adjusting future cash flows to the time value of money. This analysis assesses the present fair value of assets, projects, or companies by taking into account many factors such as inflation, risk, and cost of capital, as well as analyzing the company's future performance.read more, which calculates the present value of a firm by discounting future cash flows by the expected rate of return to its equity and debt holders.

- The cost of debt may be determined before tax or after tax.
- The total interest expense incurred by a firm in any particular year is its before-tax Kd.
- The total interest expense upon total debt availed by the company is the expected rate of return (before tax).
- Since interest expensesInterest ExpensesInterest expense is the amount of interest payable on any borrowings, such as loans, bonds, or other lines of credit, and the costs associated with it are shown on the income statement as interest expense.read more are deductible from taxable income resulting in savings for the firm, which is available to the debt holder, the after-tax cost of debt is considered for determining the effective interest rate in DCF methodology.
- The after-tax Kd is determined by netting off the amount saved in tax from interest expense.

### Cost of Debt Formula (Kd)

The formula for determining the Pre-tax Kd is as follows:

**Cost of Debt**

_{Pre-tax}Formula = (Total Interest Cost Incurred / Total Debt )*100The formula for determining the Post-tax cost of debt is as follows:

**Cost of Debt**

_{Post-tax}Formula = [(Total interest cost incurred * (1- Effective tax rate)) / Total debt] *100 You are free to use this image on your website, templates etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked

For eg:

Source: Cost of Debt (wallstreetmojo.com)

To calculate the cost of debt of a firm, the following components are to be determined:

- Total interest cost: Aggregate of interest expenses incurred by a firm in a year
- Total debt: Aggregate debt at the end of a fiscal yearFiscal YearFiscal Year (FY) is referred to as a period lasting for twelve months and is used for budgeting, account keeping and all the other financial reporting for industries. Some of the most commonly used Fiscal Years by businesses all over the world are: 1st January to 31st December, 1st April to 31st March, 1st July to 30th June and 1st October to 30th Septemberread more
- Effective tax rateEffective Tax RateEffective tax rate determines the average taxation rate for a corporation or an individual. For both, there is a similar formula only with variation in considering variables. The effective tax rate formula for corporation = Total tax expense / EBTread more: Average rate at which a firm is taxed on its’s profits

### Examples

#### Example #1

For example, if a firm has availed a long term loan of $100 at a 4% interest rate, p.a, and a $200 bond at 5% interest rate p.a. Cost of debt of the firm before tax is calculated as follows:

(4%*100+5%*200)/(100+200) *100, i.e 4.6%.

Assuming an effective tax rate of 30%, after-tax cost of debt works out to 4.6% * (1-30%)= 3.26%.

#### Example #2

Let us look at a practical example for the calculation of the cost of debt. Suppose a firm has subscribed to a $1000 bond repayable in 5 years at an interest rate of 5%. The yearly interest expense incurred by the company would be as follows:

i.e., the interest expense paid by the firm in 1 year is $50. Savings on tax at an effective tax rate of 30% would be as follows:

i.e., the firm has deducted $15 from taxable income. Hence the interest expense net of taxNet Of TaxThe term "net of taxes" refers to the amount remaining after deducting taxes. Net of taxes = Gross amount – Tax amountread more works out to $50-$15=$35. The post-tax cost of debt is calculated as follows:

#### Example #3

For DCF valuation, determination of cost of debt based on the latest issue of bonds/loans availed by the firm (i.e., the interest rate on bonds v/s debt availed) may be considered. This indicates the riskiness of the firm perceived by the market and is, therefore, a better indicator of expected returns to the debt holder.

Where the market value of a bond is available, Kd may be determined from yield to maturity (YTM) of the bond, which is the present value of all the cash flows from the bond issuance, which is equivalent to the pre-tax cost of debt.

For example, if a firm has determined that it could issue semi-annual bonds of face value $1000 and a market value of $ 1050, with an 8% coupon rate (paid semi-annually) maturing in 10 years, then it’s the before-tax cost of debt. It is calculated by solving the equation for r.

**Bond price= PMT/(1+r) ^ ^{1}+ PMT/(1+r) ^^{2}+…..+ PMT/(1+r)^^{n}+ FV/(1+r)^^{n}**

i.e

The semi-annual interest payment is

- = 8%/2 * $1000
- = $40

Putting this value in the above-given formula we get the following equation,

1050 = 40/(1+r)^^{1}+ 40/(1+r)^^{2}+…..+ 40/(1+r)^^{20}+ 1000/(1+r)^^{20}

Solving for the above formula using a financial calculator or excel, we get r= 3.64%

So, Kd (Before -tax) is

- = r*2 (since r is calculated for semi-annual coupon payments)
- = 7.3%

Kd (Post-tax) is determined as

- 7.3% * (1- effective tax rate)
- = 7.3%*(1-30%)
- = 5.1%.

The YTMYTMYield to Maturity refers to the expected returns an investor anticipates after keeping the bond intact till the maturity date. In other words, a bond's expected returns after making all the payments on time throughout the life of a bond.read more incorporates the impact of changes in market rates on a firm’s cost of debt.

### Advantages

- An optimum mix of debt and equity determines the overall savings to the firm. In the above example, if the bonds of $1000 were utilized in investments that would generate return more than 4%, then the firm has generated profits from the funds availed.
- It is an effective indicator of the adjusted rate paid by the firms and thus aids in making debt/equity funding decisions. Comparing the cost of debt to the expected growth in income resulting from the capital investmentCapital InvestmentCapital Investment refers to any investments made into the business with the objective of enhancing the operations. It could be long term acquisition by the business such as real estates, machinery, industries, etc.read more would provide an accurate picture of the overall returns from the funding activity.

### Disadvantages

- The firm is obligated to pay back the principal borrowed along with interest. Failure to pay back debt obligations results in a levy of penal interest on arrears.
- The firm may also be required to earmark cash/FD’s against such payment obligations, which would impact free cash flows available for daily operations.
- Non-payment of debt obligations would adversely affect the overall creditworthiness of the firm.

### Limitations

- Calculations do not factor in other charges incurred for debt financing, such as credit underwriting charges, fees, etc.
- The formula assumes no change in the capital structure of the firm during the period under review.
- To understand the overall rate of return to the debt holders, interest expenses on creditors and current liabilities should also be considered.

An increase in the cost of debt of a firm is an indicator of an increase in riskiness associated with its operations. The higher the cost of debt, the riskier the firm.

In order to make a final decision on the valuation of a firm, the weighted average cost of capital (comprising of cost of debt and equity) should be read along with valuation ratios such as Enterprise valueEnterprise ValueEnterprise Value is a measure of a company's total value that spans the entire market rather than just the equity value. It includes all debt and equity-based ownership claims. This value, which is calculated as the market value of debt + market value of equity - cash and cash equivalents, is particularly relevant when valuing a takeover.read more and Equity value of the firmEquity Value Of The FirmEquity Value, also known as market capitalization, is the sum-total of the values the shareholders have made available for the business and can be calculated by multiplying the market value per share by the total number of shares outstanding.read more.

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